This current study is a randomised prospective phase II study of pre-emptive adoptive cellular therapy for CMV following T cell depleted allogeneic HSCT from an unrelated donor. The study is based on earlier phase I-II studies of CMV-specific cellular therapy and our ongoing phase III study of CMV-specific adoptive cellular immunotherapy in immunocompromised recipients of allogeneic sibling donor HSCT based on selection of CMV-specific T cells by two different methodologies (CMV-IMPACT). The proof of safety in the sibling donor setting now strengthens the case for extending the therapy to the unrelated donor setting, where both potential risks and benefits are greater. The current study will investigate the use of CMV-specific T cells selected from mobilised blood collected at the time of stem cell apheresis by the multimer technology in the unrelated donor setting. The selection of CMV-specific T cells selected from a mobilised blood at the time of stem cell apheresis is in contrast to the methodology used in the CMV-IMPACT study where selection is performed on a non-mobilised blood product produced from a second study-dedicated apheresis. Two significant issues remain unresolved for the CMV-ACE/ASPECT study; are these infusions safe in the HLA-matched un-related donor setting and do CMV-reactive T cells derived from the transplant product have equivalent activity in vivo to cells derived from a second apheresis as used in the sibling donor study (CMV-IMPACT study). The study will test the hypothesis that ACT can augment the impaired CMV immune function post-transplant and reduce the requirement for CMV antiviral drug therapy without causing an increase in GVHD; and to determine the efficacy of pre-emptive CMV-specific adoptive cellular therapy following T cell depleted allogeneic HSCT with respect to reconstitution of CMV-reactive T cells. There are multiple methods for T cell depletion available, and differences between them will likely have an effect on immune reconstitution. The study will be restricted to patients receiving alemtuzumab-containing conditioning protocols, where the risk of CMV infection is greatest. ACT will be administered from day 21 post transplant for those receiving ex-vivo T-cell depleted grafts and day 28 for those receiving in vivo T cell depletion, as a single dose immediately upon a single CMV-DNA PCR+ result.